Lectures and office hours will be held on zoom to start the semester at the following link:

https://purdue-edu.zoom.us/j/94663689769

Piazza

Syllabus, policies, and procedures

Similar courses elsewhere

Randomized Algorithms.
David Karger (MIT).

Randomized Algorithms.
Sariel Har-Peled (UIUC).

Randomness and Computation.
Alistair Sinclair (Berkeley).

Algorithms for Big Data.
Jelani Nelson (Harvard).

Algorithms for Big Data.
Chandra Chekuri (UIUC).

Randomized Algorithms.
Avrim Blum and Anupam Gupta (CMU).

Advanced algorithms.
Ankur Moitra (MIT).

Pseudorandomness.
Salil Vadhan (Harvard).

Randomized Algorithms and Probabilistic Analysis.
Greg Valiant (Stanford).

Textbook: Randomized Algorithms, by Motwani and Raghavan

Other recommended texts include Probability and Computing, by Mitzenmacher and Upfal; and The Probabilistic Method, by Alon and Spencer

Key dates

Midterm and final are both TBD

Calendar

TuesdayThursday
8/25Heavy hitters8/27Linear probing

Homework A

Notes on basic probability by Chandra Chekuri; Cormode and Muthukrishnan (2005); Notes from Fall '19 randomized algorithms class; Notes by Moses Charikar; Video lecture by Ankur Moitra; Video lecture by Jelani Nelson; Notes by Chandra Chekuri; Notes from Spring '20 algorithms class on universal hashing

Homework B

Handwritten notes from lecture; Knuth (1963); Pagh, Pagh, and Ruzic (2006); Notes by Mikkel Thorup; Video from Spring 2020; Video by Jelani

9/1Distinct elements9/3Dimensionality reduction

Homework C

Handwritten notes from class; Flajolet, Martin (1985); Alon, Matias, Szegedy (1996); Notes by Chandra Chekuri; Notes by Moses Charikar; Notes by Jelani

Homework D

Handwritten notes from class; Chapter 2 of book by Blum, Hopcroft, Kannan (2018); Notes by Sariel Har-Peled; Video by Ankur Moitra; Cohen, Jayram, Nelson (2018); Indyk (2001)

9/8Locality Sensitive Hashing9/10Min cuts and sparsification

Homework E

Handwritten notes from class; Indyk, Motwani (1998); Charikar (2004); Har-Peled, Indyk, Motwani (2012); Andoni and Indyk (2008 survey); Slides by Piotr Indyk; Slides by Chandra Chekuri; Notes by Sanjoy Dasgupta; Notes by Ankur Moitra

Homework F

Handwritten notes from class; Handwritten notes from Fall 2019; Nagamochi and Ibaraki (1992); Karger (1993); Karger and Stein (1996); Karger's thesis (1995)

9/15Sparsification9/17Flow and MST

Homework G

Handwritten notes from class; Benczur and Karger (2015); Fung, Hariharan, Harvey, Panigrahi (2019)

Homework H

Handwritten notes from class; Karger, Klein, and Tarjan (1995); Dixon, Rauch, Tarjan (1992); King (1997); Buchsbaum et al.

9/22Randomized rounding9/24Metric tree embeddings

Homework I

Video from Spring 2020; Handwritten notes prepared before class; Handwritten notes from class; Notes by Avrim Blum; Notes by Anupam Gupta; Slides by Chandra Chekuri; Original paper by Raghavan and Thompson; Technical report by Raghavan and Thompson

Homework J

Handwritten notes from class; Bartal (1996); Bartal (1998); Fakcharoenphol, Rao, Talwar (2004); Handwritten notes from Fall 2019; Notes by Anupam Gupta; Notes by Avrim Blum

9/29LP duality and oblivious routing10/1Line embeddings and sparsest cut

Homework K

Handwritten notes from class; Räcke (2008)

Homework L

Handwritten notes from class; Chapter 16 in Shmoys-Williamson; Video from Spring 2020; Notes by Avrim Blum; Notes by David Karger; Notes by Shayan Oveis Gharan

10/6Two theorems by Claude Shannon10/8Entropy and Coding

Homework M

Handwritten notes from class; Shannon (1948); Shannon (1949); Section 15.1 in Alon and Spencer; Notes by Sariel Har-Peled; 1971 article on entropy in Scientific American; Chapter 6 in Guruswami, Rudra, Sudhan; Survey by Radhakrishnan; Chapter 10 in Mitzenmacher and Upfal

Homework N

Handwritten notes from class

10/13A linear map of the web10/15Electrical networks and random walks

Homework O

Handwritten notes from class; Brin, Page, Motwani, Winograd (1998); Brin, Page (1998); Brin, Page, Motwani, Winograd (1999); Notes by Dan Spielman; Section 4.8 of Blum, Hopcroft, Kannan

Homework P

Handwritten notes from class; Doyle and Snell (1984); Section 4.5 in Blum, Hopcroft, Kannan; Section 2.4 in Vadhan; Chapters 10 and 11 in Spielman's book

10/20Electrical networks and the graph Laplacian10/22The spectral theorem and convergence rates of random walks

Homework Q

Handwritten notes from class; Chapter 1 in Spielman; Chapter 1 and 2 in Trevisan

Homework R

Handwritten notes from class; Chapter 10 in Spielman; Chapter 3 in Hoory, Linial, Wigderson; Video by Gilbert Strang on symmetric matrices

10/27Spectral embeddings and sparsest cut10/29(De-)randomized connectivity with logarithmic space

Homework S

Handwritten notes from class; Section 4.4 in Hoory, Linial and Wigderson (2006); Chapter 4 in Trevisan

Handwritten notes from class; Sections 4.3 - 4.4 in Vadhan (2012); Section 9.5 in Hoory, Linial, and Wigderson (2006)

11/3Deterministic connectivity (cont'd)11/5Derandomization by random walks

Handwritten notes from class; Sections 4.3 - 4.4 in Vadhan (2012); Section 9.5 in Hoory, Linial, and Wigderson (2006)

Homework T

Handwritten notes from class; Sections 4.1 - 4.2 in Vadhan (2012); Section 3.2 in Hoory, Linial, and Wigderson (2006)

11/10Derandomization by random walks (cont'd)11/12Verifying proofs with random walks

Homework U

Handwritten notes from class; Sections 4.1 - 4.2 in Vadhan (2012); Section 3.2 in Hoory, Linial, and Wigderson (2006)

Homework V

Dinur (2006); Radhakrishnan and Sudhan (2006); Radhakrishnan (2006); Notes by Praladh Harsha; Notes by Dana Moshkovitz; Video lecture by Praladh Harsha

11/17Verifying proofs with random walks11/19Verifying proofs with random walks

Homework W

Dinur (2006); Radhakrishnan and Sudhan (2006); Radhakrishnan (2006); Notes by Praladh Harsha; Notes by Dana Moshkovitz; Video lecture by Praladh Harsha

Dinur (2006); Radhakrishnan and Sudhan (2006); Radhakrishnan (2006); Notes by Praladh Harsha; Notes by Dana Moshkovitz; Video lecture by Praladh Harsha

12/1Randomly testing boolean functions12/3Random graphs

Book by Ryan O'Donnell

Erdős and Rényi (1960); Bollobas (1984); Karp (1990); Notes by Alistair Sinclair; Article by Joel Spencer; Chapter 7 of book by Bollobas

12/8